Solvability of second-order coupled systems on the half-line

Minhós, Feliz; Sousa, Robert de

doi:10.1007/s10986-019-09419-y

Cited by 5 publications

(2 citation statements)

References 22 publications

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“…Coupled systems of second-order differential equations, where there is dependence between the various unknown variables, were studied in a huge variety of theoretical and applied situations involving different types of boundary conditions, such as [14][15][16][17]. Moreover, there are many real phenomena modeled by coupled systems, particularly in problems related to population dynamics, as in [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Ambrosetti–Prodi Alternative for Coupled and Independent Systems of Second-Order Differential Equations

Minhós,

Rodrigues

2023

Mathematics

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This paper deals with two types of systems of second-order differential equations with parameters: coupled systems with the boundary conditions of the Sturm–Liouville type and classical systems with Dirichlet boundary conditions. We discuss an Ambosetti–Prodi alternative for each system. For the first type of system, we present sufficient conditions for the existence and non-existence of its solutions, and for the second type of system, we present sufficient conditions for the existence and non-existence of a multiplicity of its solutions. Our arguments apply the lower and upper solutions method together with the properties of the Leary–Schauder topological degree theory. To the best of our knowledge, the present study is the first time that the Ambrosetti–Prodi alternative has been obtained for such systems with different parameters.

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Section: Introductionmentioning

confidence: 99%

Ambrosetti–Prodi Alternative for Coupled and Independent Systems of Second-Order Differential Equations

Minhós,

Rodrigues

2023

Mathematics

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“…Inspired by these works, we follow arguments and techniques considered in [15] and [17], in particular, about impulsive problems on the half-line and second order coupled systems on the half-line, respectively. However, it is the first time where the existence of solutions is obtained for impulsive coupled systems, with generalized jump conditions in half-line and with full nonlinearities, that depend on the unknown functions and their first derivatives.…”

Section: Introductionmentioning

confidence: 99%

Existence result for impulsive coupled systems on the half-line

Minhós

Sousa

2018

RACSAM

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This work considers a second order impulsive coupled system of differential equations with generalized jump conditions in half-line, which can depend on the impulses of the unknown functions and their first derivatives.The arguments apply the fixed point theory, Green's functions technique, L 1 -Carathéodory functions and sequences and Schauder's fixed point theorem.The method is based on Carathéodory concept of functions and sequences, together with the equiconvergence on infinity and on each impulsive moment, and it allows to consider coupled fully nonlinearities and very general impulsive functions.

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Periodic second-order systems and coupled forced Van der Pol oscillators

Minhós,

Perestrelo

2024

J. Fixed Point Theory Appl.

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We present an existence and localization result for periodic solutions of second-order non-linear coupled planar systems, without requiring periodicity for the non-linearities. The arguments for the existence tool are based on a variation of the Nagumo condition and the Topological Degree Theory. The localization tool is based on a technique of orderless upper and lower solutions, that involves functions with translations. We apply our result to a system of two coupled Van der Pol oscillators with a forcing component.

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Solvability of second-order coupled systems on the half-line

Cited by 5 publications

References 22 publications

Ambrosetti–Prodi Alternative for Coupled and Independent Systems of Second-Order Differential Equations

Ambrosetti–Prodi Alternative for Coupled and Independent Systems of Second-Order Differential Equations

Existence result for impulsive coupled systems on the half-line

Periodic second-order systems and coupled forced Van der Pol oscillators

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